SMALL SOLUTIONS TO NONLINEAR SCHRODINGER-EQUATIONS

被引：213

作者：

KENIG, CE

PONCE, G

VEGA, L

机构：

[1] UNIV CALIF SANTA BARBARA,DEPT MATH,SANTA BARBARA,CA 93106

[2] UNIV AUTONOMA MADRID,FAC CIENCIAS,MADRID 28049,SPAIN

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 1993年 / 10卷 / 03期

关键词：

NONLINEAR SCHRODINGER EQUATIONS; SMOOTHING EFFECTS;

D O I：

10.1016/S0294-1449(16)30213-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that the initial value problem for the nonlinear Schrodinger equations partial derivative(t)u = iDELTAu + P(u, del(x), u, uBAR, del(x) uBAR), t is-an-element-of R, x is-an-element-of R(n), where P(.) is a polynomial having no constant or linear terms, is locally well posed for a class of ''small'' data u0. The main ingredients in the proof are new estimates describing the smoothing effect of Kato type for the group {e(itDELTA)}-infinity(infinity). This method extends to systems and other dispersive models.

引用

页码：255 / 288

页数：34

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[11] UNIQUENESS OF SOLUTIONS FOR THE GENERALIZED KORTEWEG-DEVRIES EQUATION [J].